write an absolute value equation that represents the graph shown.\nyour answer should use the form |x - a| =…

Explanation:

Step1: Find the mid - point

The two points on the number - line are $x=-2$ and $x = 5$. The mid - point $a$ of two numbers $x_1$ and $x_2$ is given by $a=\frac{x_1 + x_2}{2}=\frac{-2 + 5}{2}=\frac{3}{2}$.

Step2: Find the distance

The distance $b$ from the mid - point to either of the points is $b=\left|5-\frac{3}{2}\right|=\left|\frac{10 - 3}{2}\right|=\frac{7}{2}$.

Step3: Write the absolute - value equation

The absolute - value equation of the form $|x - a|=b$ is $\left|x-\frac{3}{2}\right|=\frac{7}{2}$.

Answer:

$\left|x-\frac{3}{2}\right|=\frac{7}{2}$